STEADY COMPRESSIBLE VORTEX FLOWS - THE HOLLOW-CORE VORTEX ARRAY

We examine the effects of compressiblity on the structure of a single row of hollow-core, constant-pressure vortices. The problem is formulated and solved in the hodograph plane. The transformation from the physical plane to the hodograph plane results in a linear problem that is solved numerically. The numerical solution is checked via a Rayleigh-Janzen expansion. It is observed that for an appropriate choice of the parameters M(infinity) = q(infinity)/c(infinity), and the speed ratio, a = q(infinity)/q(v), where q(v) is the speed on the vortex boundary, transonic shock-free flow exists. Also, for a given fixed speed ratio, a, the vortices shrink in size and get closer as the Mach number at infinity, M(infinity), is increased. In the limit of an evacuated vortex core, we find that all such solutions exhibit cuspidal behaviour corresponding to the onset of limit lines.